1/* 2 * Copyright (c) 1983 Regents of the University of California. 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice, this list of conditions and the following disclaimer. 10 * 2. Redistributions in binary form must reproduce the above copyright 11 * notice, this list of conditions and the following disclaimer in the 12 * documentation and/or other materials provided with the distribution. 13 * 3. [rescinded 22 July 1999] 14 * 4. Neither the name of the University nor the names of its contributors 15 * may be used to endorse or promote products derived from this software 16 * without specific prior written permission. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 28 * SUCH DAMAGE. 29 */ 30 31/* 32 * This is derived from the Berkeley source: 33 * @(#)random.c 5.5 (Berkeley) 7/6/88 34 * It was reworked for the GNU C Library by Roland McGrath. 35 */ 36 37/* 38 39@deftypefn Supplement {long int} random (void) 40@deftypefnx Supplement void srandom (unsigned int @var{seed}) 41@deftypefnx Supplement void* initstate (unsigned int @var{seed}, @ 42 void *@var{arg_state}, unsigned long @var{n}) 43@deftypefnx Supplement void* setstate (void *@var{arg_state}) 44 45Random number functions. @code{random} returns a random number in the 46range 0 to @code{LONG_MAX}. @code{srandom} initializes the random 47number generator to some starting point determined by @var{seed} 48(else, the values returned by @code{random} are always the same for each 49run of the program). @code{initstate} and @code{setstate} allow fine-grained 50control over the state of the random number generator. 51 52@end deftypefn 53 54*/ 55 56#include <errno.h> 57 58#if 0 59 60#include <ansidecl.h> 61#include <limits.h> 62#include <stddef.h> 63#include <stdlib.h> 64 65#else 66 67#define ULONG_MAX ((unsigned long)(~0L)) /* 0xFFFFFFFF for 32-bits */ 68#define LONG_MAX ((long)(ULONG_MAX >> 1)) /* 0x7FFFFFFF for 32-bits*/ 69 70#ifdef __STDC__ 71# define PTR void * 72# ifndef NULL 73# define NULL (void *) 0 74# endif 75#else 76# define PTR char * 77# ifndef NULL 78# define NULL (void *) 0 79# endif 80#endif 81 82#endif 83 84long int random (void); 85 86/* An improved random number generation package. In addition to the standard 87 rand()/srand() like interface, this package also has a special state info 88 interface. The initstate() routine is called with a seed, an array of 89 bytes, and a count of how many bytes are being passed in; this array is 90 then initialized to contain information for random number generation with 91 that much state information. Good sizes for the amount of state 92 information are 32, 64, 128, and 256 bytes. The state can be switched by 93 calling the setstate() function with the same array as was initiallized 94 with initstate(). By default, the package runs with 128 bytes of state 95 information and generates far better random numbers than a linear 96 congruential generator. If the amount of state information is less than 97 32 bytes, a simple linear congruential R.N.G. is used. Internally, the 98 state information is treated as an array of longs; the zeroeth element of 99 the array is the type of R.N.G. being used (small integer); the remainder 100 of the array is the state information for the R.N.G. Thus, 32 bytes of 101 state information will give 7 longs worth of state information, which will 102 allow a degree seven polynomial. (Note: The zeroeth word of state 103 information also has some other information stored in it; see setstate 104 for details). The random number generation technique is a linear feedback 105 shift register approach, employing trinomials (since there are fewer terms 106 to sum up that way). In this approach, the least significant bit of all 107 the numbers in the state table will act as a linear feedback shift register, 108 and will have period 2^deg - 1 (where deg is the degree of the polynomial 109 being used, assuming that the polynomial is irreducible and primitive). 110 The higher order bits will have longer periods, since their values are 111 also influenced by pseudo-random carries out of the lower bits. The 112 total period of the generator is approximately deg*(2**deg - 1); thus 113 doubling the amount of state information has a vast influence on the 114 period of the generator. Note: The deg*(2**deg - 1) is an approximation 115 only good for large deg, when the period of the shift register is the 116 dominant factor. With deg equal to seven, the period is actually much 117 longer than the 7*(2**7 - 1) predicted by this formula. */ 118 119 120 121/* For each of the currently supported random number generators, we have a 122 break value on the amount of state information (you need at least thi 123 bytes of state info to support this random number generator), a degree for 124 the polynomial (actually a trinomial) that the R.N.G. is based on, and 125 separation between the two lower order coefficients of the trinomial. */ 126 127/* Linear congruential. */ 128#define TYPE_0 0 129#define BREAK_0 8 130#define DEG_0 0 131#define SEP_0 0 132 133/* x**7 + x**3 + 1. */ 134#define TYPE_1 1 135#define BREAK_1 32 136#define DEG_1 7 137#define SEP_1 3 138 139/* x**15 + x + 1. */ 140#define TYPE_2 2 141#define BREAK_2 64 142#define DEG_2 15 143#define SEP_2 1 144 145/* x**31 + x**3 + 1. */ 146#define TYPE_3 3 147#define BREAK_3 128 148#define DEG_3 31 149#define SEP_3 3 150 151/* x**63 + x + 1. */ 152#define TYPE_4 4 153#define BREAK_4 256 154#define DEG_4 63 155#define SEP_4 1 156 157 158/* Array versions of the above information to make code run faster. 159 Relies on fact that TYPE_i == i. */ 160 161#define MAX_TYPES 5 /* Max number of types above. */ 162 163static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 164static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 165 166 167 168/* Initially, everything is set up as if from: 169 initstate(1, randtbl, 128); 170 Note that this initialization takes advantage of the fact that srandom 171 advances the front and rear pointers 10*rand_deg times, and hence the 172 rear pointer which starts at 0 will also end up at zero; thus the zeroeth 173 element of the state information, which contains info about the current 174 position of the rear pointer is just 175 (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */ 176 177static long int randtbl[DEG_3 + 1] = 178 { TYPE_3, 179 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 180 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb, 181 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 182 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 183 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7, 184 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 185 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 186 0xf5ad9d0e, 0x8999220b, 0x27fb47b9 187 }; 188 189/* FPTR and RPTR are two pointers into the state info, a front and a rear 190 pointer. These two pointers are always rand_sep places aparts, as they 191 cycle through the state information. (Yes, this does mean we could get 192 away with just one pointer, but the code for random is more efficient 193 this way). The pointers are left positioned as they would be from the call: 194 initstate(1, randtbl, 128); 195 (The position of the rear pointer, rptr, is really 0 (as explained above 196 in the initialization of randtbl) because the state table pointer is set 197 to point to randtbl[1] (as explained below).) */ 198 199static long int *fptr = &randtbl[SEP_3 + 1]; 200static long int *rptr = &randtbl[1]; 201 202 203 204/* The following things are the pointer to the state information table, 205 the type of the current generator, the degree of the current polynomial 206 being used, and the separation between the two pointers. 207 Note that for efficiency of random, we remember the first location of 208 the state information, not the zeroeth. Hence it is valid to access 209 state[-1], which is used to store the type of the R.N.G. 210 Also, we remember the last location, since this is more efficient than 211 indexing every time to find the address of the last element to see if 212 the front and rear pointers have wrapped. */ 213 214static long int *state = &randtbl[1]; 215 216static int rand_type = TYPE_3; 217static int rand_deg = DEG_3; 218static int rand_sep = SEP_3; 219 220static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])]; 221 222/* Initialize the random number generator based on the given seed. If the 223 type is the trivial no-state-information type, just remember the seed. 224 Otherwise, initializes state[] based on the given "seed" via a linear 225 congruential generator. Then, the pointers are set to known locations 226 that are exactly rand_sep places apart. Lastly, it cycles the state 227 information a given number of times to get rid of any initial dependencies 228 introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 229 for default usage relies on values produced by this routine. */ 230void 231srandom (unsigned int x) 232{ 233 state[0] = x; 234 if (rand_type != TYPE_0) 235 { 236 register long int i; 237 for (i = 1; i < rand_deg; ++i) 238 state[i] = (1103515145 * state[i - 1]) + 12345; 239 fptr = &state[rand_sep]; 240 rptr = &state[0]; 241 for (i = 0; i < 10 * rand_deg; ++i) 242 random(); 243 } 244} 245 246/* Initialize the state information in the given array of N bytes for 247 future random number generation. Based on the number of bytes we 248 are given, and the break values for the different R.N.G.'s, we choose 249 the best (largest) one we can and set things up for it. srandom is 250 then called to initialize the state information. Note that on return 251 from srandom, we set state[-1] to be the type multiplexed with the current 252 value of the rear pointer; this is so successive calls to initstate won't 253 lose this information and will be able to restart with setstate. 254 Note: The first thing we do is save the current state, if any, just like 255 setstate so that it doesn't matter when initstate is called. 256 Returns a pointer to the old state. */ 257PTR 258initstate (unsigned int seed, PTR arg_state, unsigned long n) 259{ 260 PTR ostate = (PTR) &state[-1]; 261 262 if (rand_type == TYPE_0) 263 state[-1] = rand_type; 264 else 265 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 266 if (n < BREAK_1) 267 { 268 if (n < BREAK_0) 269 { 270 errno = EINVAL; 271 return NULL; 272 } 273 rand_type = TYPE_0; 274 rand_deg = DEG_0; 275 rand_sep = SEP_0; 276 } 277 else if (n < BREAK_2) 278 { 279 rand_type = TYPE_1; 280 rand_deg = DEG_1; 281 rand_sep = SEP_1; 282 } 283 else if (n < BREAK_3) 284 { 285 rand_type = TYPE_2; 286 rand_deg = DEG_2; 287 rand_sep = SEP_2; 288 } 289 else if (n < BREAK_4) 290 { 291 rand_type = TYPE_3; 292 rand_deg = DEG_3; 293 rand_sep = SEP_3; 294 } 295 else 296 { 297 rand_type = TYPE_4; 298 rand_deg = DEG_4; 299 rand_sep = SEP_4; 300 } 301 302 state = &((long int *) arg_state)[1]; /* First location. */ 303 /* Must set END_PTR before srandom. */ 304 end_ptr = &state[rand_deg]; 305 srandom(seed); 306 if (rand_type == TYPE_0) 307 state[-1] = rand_type; 308 else 309 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 310 311 return ostate; 312} 313 314/* Restore the state from the given state array. 315 Note: It is important that we also remember the locations of the pointers 316 in the current state information, and restore the locations of the pointers 317 from the old state information. This is done by multiplexing the pointer 318 location into the zeroeth word of the state information. Note that due 319 to the order in which things are done, it is OK to call setstate with the 320 same state as the current state 321 Returns a pointer to the old state information. */ 322 323PTR 324setstate (PTR arg_state) 325{ 326 register long int *new_state = (long int *) arg_state; 327 register int type = new_state[0] % MAX_TYPES; 328 register int rear = new_state[0] / MAX_TYPES; 329 PTR ostate = (PTR) &state[-1]; 330 331 if (rand_type == TYPE_0) 332 state[-1] = rand_type; 333 else 334 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 335 336 switch (type) 337 { 338 case TYPE_0: 339 case TYPE_1: 340 case TYPE_2: 341 case TYPE_3: 342 case TYPE_4: 343 rand_type = type; 344 rand_deg = degrees[type]; 345 rand_sep = seps[type]; 346 break; 347 default: 348 /* State info munged. */ 349 errno = EINVAL; 350 return NULL; 351 } 352 353 state = &new_state[1]; 354 if (rand_type != TYPE_0) 355 { 356 rptr = &state[rear]; 357 fptr = &state[(rear + rand_sep) % rand_deg]; 358 } 359 /* Set end_ptr too. */ 360 end_ptr = &state[rand_deg]; 361 362 return ostate; 363} 364 365/* If we are using the trivial TYPE_0 R.N.G., just do the old linear 366 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the 367 same in all ther other cases due to all the global variables that have been 368 set up. The basic operation is to add the number at the rear pointer into 369 the one at the front pointer. Then both pointers are advanced to the next 370 location cyclically in the table. The value returned is the sum generated, 371 reduced to 31 bits by throwing away the "least random" low bit. 372 Note: The code takes advantage of the fact that both the front and 373 rear pointers can't wrap on the same call by not testing the rear 374 pointer if the front one has wrapped. Returns a 31-bit random number. */ 375 376long int 377random (void) 378{ 379 if (rand_type == TYPE_0) 380 { 381 state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX; 382 return state[0]; 383 } 384 else 385 { 386 long int i; 387 *fptr += *rptr; 388 /* Chucking least random bit. */ 389 i = (*fptr >> 1) & LONG_MAX; 390 ++fptr; 391 if (fptr >= end_ptr) 392 { 393 fptr = state; 394 ++rptr; 395 } 396 else 397 { 398 ++rptr; 399 if (rptr >= end_ptr) 400 rptr = state; 401 } 402 return i; 403 } 404} 405